how many sigfigs in 16.58

Lussy04

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22-01-2025

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Determining the number of significant figures (sig figs) in a number is crucial for accurate scientific calculations and reporting. Understanding sig figs ensures that your results reflect the precision of your measurements. Let's figure out how many significant figures are in the number 16.58.

Understanding Significant Figures

Significant figures represent the digits in a number that carry meaning contributing to its precision. They're important because they indicate the level of uncertainty in a measurement. A measurement of 16.58 cm is more precise than a measurement of 17 cm.

Rules for Determining Significant Figures

Several rules guide the determination of significant figures:

• Non-zero digits are always significant. The digits 1, 6, 5, and 8 in 16.58 are all non-zero and therefore significant.

• Zeros between non-zero digits are significant. If we had a number like 1005, the zero between 1 and 5 would be significant. However, this doesn't apply to 16.58.

• Leading zeros (zeros to the left of the first non-zero digit) are not significant. For example, in 0.0012, the leading zeros are not significant.

• Trailing zeros (zeros to the right of the last non-zero digit) are significant only if the number contains a decimal point. In the number 100, the zeros are not significant because there is no decimal. But in 100.0, they are. Again, this doesn't apply to 16.58, as it has a decimal.

• Trailing zeros in a number without a decimal point are ambiguous and should be avoided using scientific notation. For example, writing 100 in scientific notation as 1.00 x 10² clearly indicates two significant figures.

Answer: The Number of Significant Figures in 16.58

Applying the rules above, we can easily determine the number of significant figures in 16.58:

All digits in 16.58 are significant because they are either non-zero digits or they are located after the decimal. Therefore, 16.58 has four significant figures.

Examples to Clarify

Let's look at a few more examples to solidify our understanding:

• 2.50: Three significant figures (the trailing zero after the decimal is significant).
• 0.004: One significant figure (leading zeros are not significant).
• 1000: Ambiguous; could be one, two, three, or four significant figures depending on the precision of measurement. Scientific notation should be used to remove ambiguity (e.g., 1.0 x 10³ indicates two sig figs).
• 100.0: Four significant figures (trailing zero after the decimal point is significant).

Conclusion

The number 16.58 has four significant figures. Understanding significant figures is crucial for accurate reporting and calculations in science and engineering. Remember the rules outlined above to correctly identify significant figures in your numbers. If you encounter numbers with trailing zeros and no decimal point, using scientific notation is recommended to avoid ambiguity.